Less than fully rational agents are hard

Start from the opposite direction

Use simple trial and error

Modeling Contribution

"Suppose first that the market price is above the equilibrium price […] There is a surplus of the good: suppliers are unable to sell all they want at the going price. […] They respond to the surplus by cutting their prices. Prices continue to fall until the market reaches the equilibrium."

Robustness Check

A seller wants to sell \(y^*\) kilos of cheese each day. Today he charged price \(p_t\) and sold \(y_t\) kilos. How should he sets tomorrow's price \(p_{t+1}\)

\(e_t = y^* -y_t\)

\(p_{t+1} = a e_t + b \sum_0^t e_{\tau} d\tau + c \frac{de_t}{d_t} + p_0\)

Absence of model knowledge

Assume unsophisticated users

Simple to code

Simple to fit

Reactive/Subsumption Architecture

Zero-Intelligence (Plus)

Probe and Adjust

Gintis

Making 50 kilos of cheese a day require action over multiple markets: milk, workers, sales. How do we generalize PID pricing over multiple markets?

How do we decide how many kilos of cheese to produce in order to maximize profits?

Profits are maximized when marginal benefits equal marginal costs

\(\text{Marginal Benefit: } p_t = w_t \text{ :Marginal Costs}\)

Use a PID controller to find how for which production target \(p_t = w_t\)

Lower Frequency

If you have market power, you need to take that into account

\(\frac{\partial \Pi}{\partial q} = 0\)

\(\frac{\Pi(q+1) - \Pi(q-1)}{2} = 0\)

PID's targets the numerical derivative of profits.

Need to be able to predict \(p(q)\) and \(w(q)\)

Linear approximation \(p(q+1) = p_t + \mu\) and \(p(q-1) = p_t - \mu\)

PI trial and error produce paired data \(p_t,y_t\)

Can run a linear regression over them to discover \(\mu_p\)

Use Kalman Filters

Gunnery Control and Norbert Wiener

"The world, understood cybernetically, was a world of goal-oriented feedback mechanisms with learning. Cybernetics,then, took computer-controlled gun control and layered it in an ontologically indiscriminate fashion across the academic disciplinary board."